Economics Optimization and Monopoly Questions

1. The production function for a competitive economy is: Y=8N+4N2-0.75 N³

Y is gross domestic product (GDP) in £ trillion (= 1012) per year, so that you can assume that the price of 1 unit of GDP is £1. N is labour input in trillion (=1012) person-hours per year.

a) Plot the marginal and average product curves for values of N from 0 to 7 in steps of 1. [30 marks]

b) Using both calculus and your chart, determine the level of total employment corresponding to the maximization of net national product (gross domestic product less expenditure on labour input) when the average wage is £5 per hour.[70 marks]

2. 

a) Invert the matrices where possible and check [30 marks]

b) Differentiate these functions with respect to X showing your steps in full) [10 marks]
 

[do not simplify your answer][10 marks]

c) A national income model is given by the equations:

C=233+0.67 (Y-T)

T=0.23 Y

M=90+0.18 Y-T

I=85;

G=215;

X=150

where Y, C, I, G, X, M, and T stand for national income, consumption, investment, government spending, exports, imports, and tax revenue respectively.

Derive the multiplier and calculate the equilibrium level of national income.[50 marks]

3. A firm is a monopolist facing the market demand curve P=24-0.6Q and it has the following total cost function relating cost, C, to output, Q.

C=7Q-0.45Q+0.09 Q³

a) At what output level does marginal cost equal average cost? 

b) Discover the firm’s breakeven output.

c) Discover the firm’s profit maximising output.

d) Calculate the elasticity of demand at the profit maximising output.